Comments on: Networks and power laws http://www.johndcook.com/blog/2008/10/19/networks-and-power-laws/ The blog of John D. Cook Sat, 11 Feb 2012 01:10:06 -0500 http://wordpress.org/?v=2.8.4 hourly 1 By: Jan Theodore Galkowski http://www.johndcook.com/blog/2008/10/19/networks-and-power-laws/comment-page-1/#comment-14109 Jan Theodore Galkowski Wed, 04 Mar 2009 23:39:24 +0000 http://www.johndcook.com/blog/?p=679#comment-14109 Yes, there's a cost to maintain links in many natural and engineered systems. For instance, if there are communities and circles of friends, they don't count much and don't exert much influence if they aren't nudged and spoken to for long periods of time. A network hub can't have arbitrarily many connections, even if a scaled-up version of the hub (think Google) can serve a bunch. But, OTOH, there are counterintuitive phenomena as well, perhaps not really networks, but phenomena of <i>large scale synchronization</i>. There's a <a href="http://www.sciencemag.org/cgi/content/abstract/323/5914/614" rel="nofollow">report in a recent issue of <i>Science</i></a> which addresses "Dynamical Quorum Sensing and Synchronization in Large Populations of Chemical Oscillators" where it seems <i>easier</i> to get components to communicate the more there are. This <i>seems</i> like a <a href="http://en.wikipedia.org/wiki/Network_effect" rel="nofollow">network effect</a> although I don't know whether or not there are actual <i>links</i> in these collections. Yes, there’s a cost to maintain links in many natural and engineered systems. For instance, if there are communities and circles of friends, they don’t count much and don’t exert much influence if they aren’t nudged and spoken to for long periods of time. A network hub can’t have arbitrarily many connections, even if a scaled-up version of the hub (think Google) can serve a bunch.

But, OTOH, there are counterintuitive phenomena as well, perhaps not really networks, but phenomena of large scale synchronization. There’s a report in a recent issue of Science which addresses “Dynamical Quorum Sensing and Synchronization in Large Populations of Chemical Oscillators” where it seems easier to get components to communicate the more there are. This seems like a network effect although I don’t know whether or not there are actual links in these collections.

]]> By: Don http://www.johndcook.com/blog/2008/10/19/networks-and-power-laws/comment-page-1/#comment-8198 Don Tue, 21 Oct 2008 17:58:10 +0000 http://www.johndcook.com/blog/?p=679#comment-8198 Interesting! If I get time I'd like to try having a ceiling on the number of connections, as in practice one person cannot know (for any reasonable definition) an unlimited number of others, and a street network or even airport network can have even fewer node-node connections. Interesting! If I get time I’d like to try having a ceiling on the number of connections, as in practice one person cannot know (for any reasonable definition) an unlimited number of others, and a street network or even airport network can have even fewer node-node connections.

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